If |{:(a+ib,c+id),(-c+id,a-ib):}|xx|{:(alpha-ibeta,gamma-idelta),(-gamma-idelta,alpha+ibeta):}|=|{:(A-iB,C-iD),(-C-iD,A+iB):}|, write down the values of A, B, C, (i=sqrt(-1)). Hence show that, the product of two sums, each of four squares, can be expressed as the sum of four squares.

If |{:(a+ib,c+id),(-c+id,a-ib):}|xx|{:(alpha-ibeta,gamma-idelta),(-gam

1.	If \|{:(a+ib,c+id),(-c+id,a-ib):}\|xx\|{:(alpha-ibeta,gamma-idelta),(-gamma-idelta,alpha+ibeta):}\|=\|{:(A-iB,C-iD),(-C-iD,A+iB):}\|, write down the values of A, B, C, (i=sqrt(-1)). Hence show that, the product of two sums, each of four squares, can be expressed as the sum of four squares.
Answer» ANSWER :`A=a ALPHA+b BETA-c GAMMA+d DELTA, B=a beta-b alpha-balpha+c delta+d gamma`, ` C=a gamma+b delta+calpha-d beta, D=a delta-b gamma-b gamma-c beta-d alpha`,

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If |{:(a+ib,c+id),(-c+id,a-ib):}|xx|{:(alpha-ibeta,gamma-idelta),(-gamma-idelta,alpha+ibeta):}|=|{:(A-iB,C-iD),(-C-iD,A+iB):}|, write down the values of A, B, C, (i=sqrt(-1)). Hence show that, the product of two sums, each of four squares, can be expressed as the sum of four squares.

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